User-Friendly Covariance Estimation for Heavy-Tailed Distributions

We offer a survey of recent results on covariance estimation for heavy-tailed distributions. By unifying ideas scattered in the literature, we propose user-friendly methods that facilitate practical implementation. Specifically, we introduce element-wise and spectrum-wise truncation operators, as well as their $M$-estimator counterparts, to robustify the sample covariance matrix. Different from the classical notion of robustness that is characterized by the breakdown property, we focus on the tail robustness which is evidenced by the connection between nonasymptotic deviation and confidence level. The key observation is that the estimators needs to adapt to the sample size, dimensionality of the data and the noise level to achieve optimal tradeoff between bias and robustness. Furthermore, to facilitate their practical use, we propose data-driven procedures that automatically calibrate the tuning parameters. We demonstrate their applications to a series of structured models in high dimensions, including the bandable and low-rank covariance matrices and sparse precision matrices. Numerical studies lend strong support to the proposed methods.Comment: 56 pages, 2 figure

A Simple Parametric Classification Baseline for Generalized Category Discovery

Generalized category discovery (GCD) is a problem setting where the goal is to discover novel categories within an unlabelled dataset using the knowledge learned from a set of labelled samples. Recent works in GCD argue that a non-parametric classifier formed using semi-supervised $k$-means can outperform strong baselines which use parametric classifiers as it can alleviate the over-fitting to seen categories in the labelled set. In this paper, we revisit the reason that makes previous parametric classifiers fail to recognise new classes for GCD. By investigating the design choices of parametric classifiers from the perspective of model architecture, representation learning, and classifier learning, we conclude that the less discriminative representations and unreliable pseudo-labelling strategy are key factors that make parametric classifiers lag behind non-parametric ones. Motivated by our investigation, we present a simple yet effective parametric classification baseline that outperforms the previous best methods by a large margin on multiple popular GCD benchmarks. We hope the investigations and the simple baseline can serve as a cornerstone to facilitate future studies. Our code is available at: https://github.com/CVMI-Lab/SimGCD.Comment: Code: https://github.com/CVMI-Lab/SimGC

UFIN: Universal Feature Interaction Network for Multi-Domain Click-Through Rate Prediction

Click-Through Rate (CTR) prediction, which aims to estimate the probability of a user clicking on an item, is a key task in online advertising. Numerous existing CTR models concentrate on modeling the feature interactions within a solitary domain, thereby rendering them inadequate for fulfilling the requisites of multi-domain recommendations in real industrial scenarios. Some recent approaches propose intricate architectures to enhance knowledge sharing and augment model training across multiple domains. However, these approaches encounter difficulties when being transferred to new recommendation domains, owing to their reliance on the modeling of ID features (e.g., item id). To address the above issue, we propose the Universal Feature Interaction Network (UFIN) approach for CTR prediction. UFIN exploits textual data to learn universal feature interactions that can be effectively transferred across diverse domains. For learning universal feature representations, we regard the text and feature as two different modalities and propose an encoder-decoder network founded on a Large Language Model (LLM) to enforce the transfer of data from the text modality to the feature modality. Building upon the above foundation, we further develop a mixtureof-experts (MoE) enhanced adaptive feature interaction model to learn transferable collaborative patterns across multiple domains. Furthermore, we propose a multi-domain knowledge distillation framework to enhance feature interaction learning. Based on the above methods, UFIN can effectively bridge the semantic gap to learn common knowledge across various domains, surpassing the constraints of ID-based models. Extensive experiments conducted on eight datasets show the effectiveness of UFIN, in both multidomain and cross-platform settings. Our code is available at https://github.com/RUCAIBox/UFIN

Kemijski sastav i reološka svojstva čvrstog jogurta dobivenog od obranog mlijeka tretiranog peroksidazom iz hrena

The aim of this work is to determine the impact of an enzymatic treatment on the fermentation and rheological properties of set yoghurt prepared from skimmed milk. Skimmed bovine milk was treated with horseradish peroxidase added at the level of 645 U per g of proteins in the presence (addition level of 7.8 mmol per L of milk) or absence of ferulic acid as a cross-linking agent, and used to prepare set yoghurt with commercial direct vat set starter culture. The evaluation showed that the treatment of skimmed milk with horseradish peroxidase enhanced its apparent viscosity, and storage and loss moduli. The prepared yoghurt contained protein, fat and total solids at 3.49–3.59, 0.46–0.52 and 15.23–15.43 %, respectively, had titratable acidity of 0.83–0.88 %, and no significant difference in the composition was found among the yoghurt samples (p>0.05). Compared to the control yoghurt, the yoghurt prepared from the milk treated with horseradish peroxidase had a higher apparent viscosity, storage and loss moduli and flow behavior indices, especially when ferulic acid was added. Yoghurt samples from the skimmed milk treated either with horseradish peroxidase only or with the additional ferulic acid treatment had better structural reversibility, because their hysteresis loop area during rheological analysis was larger (p0,05). U usporedbi s kontrolnim jogurtom, jogurt dobiven od mlijeka tretiranog peroksidazom iz hrena imao je veću prividnu viskoznost, modul pohrane i modul gubitka, te indeks tečenja, naročito nakon dodatka ferulične kiseline. Uzorci jogurta dobiveni od mlijeka tretiranog samo peroksidazom iz hrena ili kombinacijom peroksidaze i ferulične kiseline imali su bolja strukturna svojstva, tj. veću petlju histereze utvrđenu reološkom analizom

Thermal performance analysis of a solar energy storage unit encapsulated with HITEC salt/copper foam/nanoparticles composite

HITEC salt (40 wt. % NaNO2, 7 wt. % NaNO3, 53 wt. % KNO3) with a melting temperature of about 142 °C is a typical phase change material (PCM) for solar energy storage. Both aluminum oxide (Al2O3) nanopowder and metal foam were used to enhance pure HITEC salt, so as to retrieve the limitation of composite PCMs with single enhancement. The morphologies and thermo-physical properties of the composites were firstly characterized with Scanning Electron Microscope, Fourier-transform Infrared spectroscopy and Differential Scanning Calorimeter, respectively. A pilot test rig with a heater of 380 W located in the inner pipe was built, which was encapsulated with HITEC salt, nano-salt (HITEC salt seeded with 2 wt. % Al2O3 nanopowder) and salt/copper foam composite seeded with 2 wt. % Al2O3 nanopowder as storage media. Then heat storage and retrieval tests of the energy storage system were conducted both for pure HITEC salt and composite PCMs at various heating temperatures. The temperature evolutions and distributions of the PCMs at different locations were measured, including radial, angular, and axial locations, and the energy and volumetric mean powers during heat storage/retrieval processes were calculated subsequently. The results show that metal foam is generally compatible with the nano-salt. The maximum deviation of the melting/freezing phase change temperatures of the nano-salt/copper foam composite is 3.54 °C, whereas that of the nano-salt/nickel foam composite is 3.80 °C. The specific heats of the nano-salt are apparently enhanced with the addition of Al2O3 nanopowder both in solid and liquid states. The system encapsulated with the nano-salt/copper foam composite can be considerably enhanced, e.g. the time-duration of heat storage process at the heating temperature of 160 °C can be reduced by about 58.5%, compared to that of pure salt. The volumetric mean power of heat storage for the nano-salt/copper foam composite at the heating temperature of 180 °C increases to 109.32 kW/m3, compared with 53.01 kW/m3 of pure HITEC salt. The information will be helpful for solar system design, construction and application using molten salt for solar energy storage